The timely and efficient generation of detailed damage maps is of fundamental importance following disaster events to speed up first responders’ (FR) rescue activities and help trapped victims. Several works dealing with the automated detection of building damages have been published in the last decade. The increasingly widespread availability of inexpensive UAV platforms has also driven their recent adoption for rescue operations (i.e., search and rescue). Their deployment, however, remains largely limited to visual image inspection by skilled operators, limiting their applicability in time-constrained real conditions. This paper proposes a new solution to autonomously map building damages with a commercial UAV in near real-time. The solution integrates different components that allow the live streaming of the images on a laptop and their processing on the fly. Advanced photogrammetric techniques and deep learning algorithms are combined to deliver a true-orthophoto showing the position of building damages, which are already processed by the time the UAV returns to base. These algorithms have been customized to deliver fast results, fulfilling the near real-time requirements. The complete solution has been tested in different conditions, and received positive feedback by the FR involved in the EU funded project INACHUS. Two realistic pilot tests are described in the paper. The achieved results show the great potential of the presented approach, how close the proposed solution is to FR’ expectations, and where more work is still needed.